You are correct.
To travel in Europe the vehicle has to be legal in its registered country.
So a UK vehicle must always have an MOT, if it’s on the road and older than 3 years old. Even when it is outside of the UK.
The only way to avoid this is to register the vehicle in another country, and do this each year as you move around.
In some countries, e.g. France, it is not straightforward to change vehicle registration, compared to countries such as the UK.
Germany might be easier, and might be an easier location to get to each year.
In my experience it’s easiest to bring the vehicle home once a year.
Vehicles younger than 3 years do not need an MOT, if you have the budget.